Find 'Build Number'. It's location varies from devices to device, but look for menus such as 'Software Information'

Tap 'Build Number' until you see a message saying 'You are now a developer'. If you see a message saying something along the lines of 'This option has been disabled by your administrator', I'm sorry to say you will need to reset your device to use ADB. You could also talk to your administrator.

Go back to the main settings page. At the bottom, you should now see 'Developer Options'. Tap it.

A warning may display. Read it carefully, and decide at your own risk.

Scroll until you find 'USB Debugging'. Tap it. You will see another warning. Read. Decide.

Connect your device to your computer. Run adb shell. A dialog box will pop up asking if you trust your computer. Tap yes.

Congrats! It should now work.

If that doesn't work, try different cables, phones, computers, and try to find what is the problem. Google is, as always, your friend.